KerMor  0.9
Model order reduction for nonlinear dynamical systems and nonlinear approximation
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getSteadyStates.m
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1 #include "PCDIModel.m"
2 namespace models{
3 namespace pcdi{
4 
5 
6 /* (Autoinserted by mtoc++)
7  * This source code has been filtered by the mtoc++ executable,
8  * which generates code that can be processed by the doxygen documentation tool.
9  *
10  * On the other hand, it can neither be interpreted by MATLAB, nor can it be compiled with a C++ compiler.
11  * Except for the comments, the function bodies of your M-file functions are untouched.
12  * Consequently, the FILTER_SOURCE_FILES doxygen switch (default in our Doxyfile.template) will produce
13  * attached source files that are highly readable by humans.
14  *
15  * Additionally, links in the doxygen generated documentation to the source code of functions and class members refer to
16  * the correct locations in the source code browser.
17  * However, the line numbers most likely do not correspond to the line numbers in the original MATLAB source files.
18  */
19 
20 function ss = models.pcdi.PCDIModel.getSteadyStates(n,doplot) {
21 
22 if nargin < 3
23  doplot = false;
24 end
25 
26 /* Procaspase-8 to Caspase-8 reaction rate */
27 K1 = this.K1*this.tau;
28 /* Procaspase-3 to Caspase-3 reaction rate */
29 K2 = this.K2*this.tau;
30 /* IAP-Caspase 3 (de)reaction rate */
31 K3 = this.K3*this.tau;
32 /* IAP-Caspase 3 one-way (de)reaction rate */
33 K4 = this.K4*this.tau;
34 /* Caspase-8 degradation rate */
35 K5 = this.K5*this.tau;
36 /* Caspase-3 degradation rate */
37 K6 = this.K6*this.tau;
38 /* YAI degradation rate */
39 K7 = this.K7*this.tau;
40 /* IAP degradation rate */
41 K8 = this.K8*this.tau;
42 /* Pro-Caspase-8 degradation rate */
43 K9 = this.K9*this.tau;
44 /* Caspase-3 degradation rate */
45 K10 = this.K10*this.tau;
46 /* BAR - Procaspase-8 (de)reaction rate */
47 K11 = this.K11*this.tau;
48 /* BAR degradation rate */
49 K12 = this.K12*this.tau;
50 /* XAP degradation rate */
51 K13 = this.K13*this.tau;
52 /* YAI to IAP production rate */
53 Km3 = this.Km3*this.tau;
54 /* IAP production rate */
55 Km8 = this.Km8*this.tau;
56 /* Procaspase-8 production rate */
57 Km9 = this.Km9*this.tau;
58 /* Procaspase-3 production rate */
59 Km10 = this.Km10*this.tau;
60 /* XAB degradation rate */
61 Km11 = this.Km11*this.tau;
62 /* BAR production rate */
63 Km12 = this.Km12*this.tau;
64 
65 /* Koeffizient vor x */
66 a1 = (-Km8 * K2 * K10 * Km9 * K12 * Km11 * K9 * K3 * K7 * K11 * K13 * Km12 - Km8 * K2 * K10 * Km9 * K12 ^ 2 * Km11 ^ 2 * K9 * K3 * K7 * K5 - 2 * Km8 * K2 * K10 * Km9 * K12 ^ 2 * Km11 * K9 * K3 * K7 * K5 * K13 - ...
67  K6 * K9 * Km9 * K12 ^ 2 * K13 ^ 2 * K10 * K8 * K2 * Km3 * K5 - Km8 * K2 * K10 * Km9 * K12 * K13 ^ 2 * K9 * K3 * K7 * K11 * Km12 - Km8 * K2 * K10 * Km9 * K12 ^ 2 * K13 ^ 2 * K9 * K3 * K7 * K5 - ...
68  K6 * K9 * Km9 * K12 ^ 2 * K13 ^ 2 * K10 * K8 * K2 * K7 * K5 - K6 * K9 * Km9 * K12 * Km11 * K10 * K8 * K2 * Km3 * K11 * K13 * Km12 - K6 * K9 * Km9 * K12 ^ 2 * Km11 ^ 2 * K10 * K8 * K2 * Km3 * K5 - ...
69  2 * K6 * K9 * Km9 * K12 ^ 2 * Km11 * K10 * K8 * K2 * Km3 * K5 * K13 - K6 * K9 * Km9 * K12 * K13 ^ 2 * K10 * K8 * K2 * K7 * K11 * Km12 - K6 * K9 * Km9 * K12 * Km11 * K10 * K8 * K2 * K7 * K11 * K13 * Km12 - ...
70  K6 * K9 * Km9 * K12 ^ 2 * Km11 ^ 2 * K10 * K8 * K2 * K7 * K5 - 2 * K6 * K9 * Km9 * K12 ^ 2 * Km11 * K10 * K8 * K2 * K7 * K5 * K13 - K6 * K9 * Km9 * K12 * K13 ^ 2 * K10 * K8 * K2 * Km3 * K11 * Km12);
71 
72 /* Koeffizient vor x^2 */
73 a2 = (-Km8 * K2 * K10 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K3 * K7 * Km12 - 2 * Km8 * K2 * K10 * Km9 * K12 * Km11 * K9 * K3 * K7 * K5 * K11 * K13 + 2 * Km8 * K2 * K10 * K11 * K13 ^ 2 * Km12 * K9 * K3 * K7 * K5 * K12 - ...
74  2 * Km8 * K2 * K10 * Km9 * K12 * K13 ^ 2 * K9 * K3 * K7 * K5 * K11 + Km8 * K2 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K9 * K3 * K7 + 2 * Km8 * K2 * K10 * K11 * K13 * Km12 * K9 * K3 * K7 * K5 * K12 * Km11 + ...
75  Km8 * K2 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K9 * K3 * K7 + 2 * Km8 * K2 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 * K9 * K3 * K7 * K13 + Km8 * K2 * K10 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K9 * K3 * K7 - ...
76  2 * K6 * K9 * Km9 * K12 * K13 ^ 2 * K10 * K8 * K2 * Km3 * K5 * K11 - 2 * K6 * K9 * Km9 * K12 * Km11 * K10 * K8 * K2 * Km3 * K5 * K11 * K13 - 2 * K6 * K9 * Km9 * K12 * Km11 * K10 * K8 * K2 * K7 * K5 * K11 * K13 + ...
77  2 * K6 * K9 * K10 * K11 * K13 * Km12 * K8 * K2 * K7 * K5 * K12 * Km11 + 2 * K6 * K9 * K10 * K11 * K13 ^ 2 * Km12 * K8 * K2 * K7 * K5 * K12 - K6 * K9 ^ 2 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K4 * Km3 - ...
78  2 * K6 * K9 * Km9 * K12 * K13 ^ 2 * K10 * K8 * K2 * K7 * K5 * K11 - K6 * K9 * Km9 * K11 ^ 2 * K13 ^ 2 * K10 * K8 * K2 * Km3 * Km12 - K6 * K9 * Km9 * K11 ^ 2 * K13 ^ 2 * K10 * K8 * K2 * K7 * Km12 + ...
79  K6 * K9 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K8 * K2 * Km3 + 2 * K6 * K9 * K10 * K11 * K13 * Km12 * K8 * K2 * Km3 * K5 * K12 * Km11 + 2 * K6 * K9 * K10 * K11 * K13 ^ 2 * Km12 * K8 * K2 * Km3 * K5 * K12 + ...
80  K6 * K9 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K8 * K2 * K7 - K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K4 * Km3 - 2 * K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 * K4 * Km3 * K13 - ...
81  K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K4 * K7 - 2 * K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 * K4 * K7 * K13 - K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K3 * K7 - ...
82  2 * K6 * K9 ^ 2 * K10 * K11 * K13 * Km12 * K4 * Km3 * K5 * K12 * Km11 - 2 * K6 * K9 ^ 2 * K10 * K11 * K13 ^ 2 * Km12 * K4 * Km3 * K5 * K12 - K6 * K9 ^ 2 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K4 * K7 - ...
83  2 * K6 * K9 ^ 2 * K10 * K11 * K13 * Km12 * K4 * K7 * K5 * K12 * Km11 - 2 * K6 * K9 ^ 2 * K10 * K11 * K13 ^ 2 * Km12 * K4 * K7 * K5 * K12 - K6 * K9 ^ 2 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K3 * K7 - ...
84  2 * K6 * K9 ^ 2 * K10 * K11 * K13 * Km12 * K3 * K7 * K5 * K12 * Km11 - 2 * K6 * K9 ^ 2 * K10 * K11 * K13 ^ 2 * Km12 * K3 * K7 * K5 * K12 + K6 * K9 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K8 * K2 * Km3 + ...
85  2 * K6 * K9 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 * K8 * K2 * Km3 * K13 + K6 * K9 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K8 * K2 * K7 + 2 * K6 * K9 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 * K8 * K2 * K7 * K13 - ...
86  2 * K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 ^ 2 * Km11 * K3 * K7 * K13 + K6 * K9 * K10 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K8 * K2 * Km3 + K6 * K9 * K10 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K8 * K2 * K7 - ...
87  K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K4 * Km3 - K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K4 * K7 - K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K3 * K7);
88 /* Koeffizient vor x^3 */
89 a3 = (2 * K6 * K9 * K10 * K5 ^ 2 * K12 * Km11 * K8 * K2 * Km3 * K11 * K13 - 2 * K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 * K13 ^ 2 * K4 * K7 * K11 - K6 * K9 * Km9 * K11 ^ 2 * K13 ^ 2 * K10 * K8 * K2 * K7 * K5 + ...
90  2 * Km8 * K2 * K10 * K5 ^ 2 * K12 * K13 ^ 2 * K9 * K3 * K7 * K11 + 2 * K6 * K9 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 * K8 * K2 * K7 * K5 + 2 * K6 * K9 * K10 * K5 ^ 2 * K12 * K13 ^ 2 * K8 * K2 * K7 * K11 - ...
91  Km8 * K2 * K10 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K3 * K7 * K5 - 2 * K6 * K9 ^ 2 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 * K3 * K7 * K5 - 2 * K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 * Km11 * K4 * K7 * K11 * K13 - ...
92  2 * K6 * K9 ^ 2 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 * K4 * K7 * K5 + 2 * K6 * K9 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 * K8 * K2 * Km3 * K5 - 2 * K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 * Km11 * K3 * K7 * K11 * K13 - ...
93  2 * K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 * K13 ^ 2 * K4 * Km3 * K11 + 2 * Km8 * K2 * K10 * K5 ^ 2 * K12 * Km11 * K9 * K3 * K7 * K11 * K13 - 2 * K6 * K9 ^ 2 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 * K4 * Km3 * K5 + ...
94  2 * K6 * K9 * K10 * K5 ^ 2 * K12 * Km11 * K8 * K2 * K7 * K11 * K13 - 2 * K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 * K13 ^ 2 * K3 * K7 * K11 - K6 * K9 * Km9 * K11 ^ 2 * K13 ^ 2 * K10 * K8 * K2 * Km3 * K5 - ...
95  2 * K6 * K9 ^ 2 * K10 * K5 ^ 2 * K12 * Km11 * K4 * Km3 * K11 * K13 + 2 * Km8 * K2 * K10 * K11 ^ 2 * K13 ^ 2 * Km12 * K9 * K3 * K7 * K5 + 2 * K6 * K9 * K10 * K5 ^ 2 * K12 * K13 ^ 2 * K8 * K2 * Km3 * K11);
96 /* Koeffizient vor x^4 */
97 a4 = (-K6 * K9 ^ 2 * K10 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K3 * K7 + K6 * K9 * K10 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K8 * K2 * Km3 - K6 * K9 ^ 2 * K10 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K4 * Km3 - ...
98  K6 * K9 ^ 2 * K10 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K4 * K7 + Km8 * K2 * K10 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K9 * K3 * K7 + K6 * K9 * K10 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K8 * K2 * K7);
99 /* Koeffizient vor x^n */
100 an = (Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K8 * Km3 + Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K8 * K7 + Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 ^ 2 * K13 ^ 2 * K8 * Km3 + ...
101  Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 ^ 2 * K13 ^ 2 * K8 * K7 + 2 * Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 ^ 2 * Km11 * K8 * Km3 * K13 + 2 * Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 ^ 2 * Km11 * K8 * K7 * K13);
102 /* Koeffizient vor x^(n+1) */
103 anp1 = (2 * Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 * Km11 * K8 * Km3 * K11 * K13 - 2 * Km10 * K2 ^ 2 * K1 * Km9 * K12 * Km11 * K8 * Km3 * K11 * K13 * Km12 - 2 * Km10 * K2 ^ 2 * K1 * Km9 * K12 ^ 2 * Km11 ^ 2 * K8 * Km3 * K5 - ...
104  4 * Km10 * K2 ^ 2 * K1 * Km9 * K12 ^ 2 * Km11 * K8 * Km3 * K5 * K13 + 2 * Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 * Km11 * K8 * K7 * K11 * K13 - 2 * Km10 * K2 ^ 2 * K1 * Km9 * K12 * Km11 * K8 * K7 * K11 * K13 * Km12 - ...
105  2 * Km10 * K2 ^ 2 * K1 * Km9 * K12 ^ 2 * Km11 ^ 2 * K8 * K7 * K5 - 4 * Km10 * K2 ^ 2 * K1 * Km9 * K12 ^ 2 * Km11 * K8 * K7 * K5 * K13 - 2 * Km10 * K2 ^ 2 * K1 * Km9 * K12 * K13 ^ 2 * K8 * Km3 * K11 * Km12 + ...
106  2 * Km10 * K2 * K1 * Km9 * K12 ^ 2 * Km11 * K9 * K4 * Km3 * K5 * K13 + 2 * Km10 * K2 * K1 * Km9 * K12 ^ 2 * Km11 * K9 * K4 * K7 * K5 * K13 + 2 * Km10 * K2 * K1 * Km9 * K12 ^ 2 * Km11 * K9 * K3 * K7 * K5 * K13 + ...
107  2 * Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 * K13 ^ 2 * K8 * Km3 * K11 - Km8 * K2 * K1 * Km9 * K12 * Km11 * K9 * K3 * K7 * K11 * K13 * Km12 - 2 * Km10 * K2 ^ 2 * K1 * Km9 * K12 ^ 2 * K13 ^ 2 * K8 * Km3 * K5 + ...
108  2 * Km10 * K2 ^ 2 * K1 * Km9 ^ 2 * K12 * K13 ^ 2 * K8 * K7 * K11 - 2 * Km10 * K2 ^ 2 * K1 * Km9 * K12 * K13 ^ 2 * K8 * K7 * K11 * Km12 - 2 * Km10 * K2 ^ 2 * K1 * Km9 * K12 ^ 2 * K13 ^ 2 * K8 * K7 * K5 - ...
109  2 * K6 * K9 * Km9 * K12 ^ 2 * Km11 * K1 * K8 * K2 * Km3 * K5 * K13 - K6 * K9 * Km9 * K12 * Km11 * K1 * K8 * K2 * K7 * K11 * K13 * Km12 - Km8 * K2 * K1 * Km9 * K12 ^ 2 * Km11 ^ 2 * K9 * K3 * K7 * K5 - ...
110  2 * Km8 * K2 * K1 * Km9 * K12 ^ 2 * Km11 * K9 * K3 * K7 * K5 * K13 - Km8 * K2 * K1 * Km9 * K12 * K13 ^ 2 * K9 * K3 * K7 * K11 * Km12 - Km8 * K2 * K1 * Km9 * K12 ^ 2 * K13 ^ 2 * K9 * K3 * K7 * K5 - ...
111  K6 * K9 * Km9 * K12 * Km11 * K1 * K8 * K2 * Km3 * K11 * K13 * Km12 - K6 * K9 * Km9 * K12 ^ 2 * Km11 ^ 2 * K1 * K8 * K2 * Km3 * K5 - K6 * K9 * Km9 * K12 ^ 2 * Km11 ^ 2 * K1 * K8 * K2 * K7 * K5 - ...
112  2 * K6 * K9 * Km9 * K12 ^ 2 * Km11 * K1 * K8 * K2 * K7 * K5 * K13 - K6 * K9 * Km9 * K12 * K13 ^ 2 * K1 * K8 * K2 * Km3 * K11 * Km12 - K6 * K9 * Km9 * K12 ^ 2 * K13 ^ 2 * K1 * K8 * K2 * Km3 * K5 - ...
113  K6 * K9 * Km9 * K12 * K13 ^ 2 * K1 * K8 * K2 * K7 * K11 * Km12 - K6 * K9 * Km9 * K12 ^ 2 * K13 ^ 2 * K1 * K8 * K2 * K7 * K5 + Km10 * K2 * K1 * Km9 * K12 * Km11 * K9 * K4 * Km3 * K11 * K13 * Km12 + ...
114  Km10 * K2 * K1 * Km9 * K12 ^ 2 * Km11 ^ 2 * K9 * K4 * Km3 * K5 + Km10 * K2 * K1 * Km9 * K12 * Km11 * K9 * K4 * K7 * K11 * K13 * Km12 + Km10 * K2 * K1 * Km9 * K12 ^ 2 * Km11 ^ 2 * K9 * K4 * K7 * K5 + ...
115  Km10 * K2 * K1 * Km9 * K12 * Km11 * K9 * K3 * K7 * K11 * K13 * Km12 + Km10 * K2 * K1 * Km9 * K12 ^ 2 * Km11 ^ 2 * K9 * K3 * K7 * K5 + Km10 * K2 * K1 * Km9 * K12 * K13 ^ 2 * K9 * K4 * Km3 * K11 * Km12 + ...
116  Km10 * K2 * K1 * Km9 * K12 ^ 2 * K13 ^ 2 * K9 * K4 * Km3 * K5 + Km10 * K2 * K1 * Km9 * K12 * K13 ^ 2 * K9 * K4 * K7 * K11 * Km12 + Km10 * K2 * K1 * Km9 * K12 * K13 ^ 2 * K9 * K3 * K7 * K11 * Km12 + ...
117  Km10 * K2 * K1 * Km9 * K12 ^ 2 * K13 ^ 2 * K9 * K4 * K7 * K5 + Km10 * K2 * K1 * Km9 * K12 ^ 2 * K13 ^ 2 * K9 * K3 * K7 * K5);
118 /* Koeffizient vor x^(n+2) */
119 anp2 = (-2 * Km8 * K2 * K1 * Km9 * K12 * K13 ^ 2 * K9 * K3 * K7 * K5 * K11 - ...
120  Km8 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K3 * K7 * Km12 + 2 * Km8 * K2 * K1 * K11 * K13 * Km12 * K9 * K3 * K7 * K5 * K12 * Km11 + 2 * Km8 * K2 * K1 * K11 * K13 ^ 2 * Km12 * K9 * K3 * K7 * K5 * K12 + ...
121  2 * Km8 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K9 * K3 * K7 * K13 - 2 * K6 * K9 * Km9 * K12 * Km11 * K1 * K8 * K2 * Km3 * K5 * K11 * K13 - 2 * K6 * K9 * Km9 * K12 * Km11 * K1 * K8 * K2 * K7 * K5 * K11 * K13 - ...
122  2 * K6 * K9 * Km9 * K12 * K13 ^ 2 * K1 * K8 * K2 * Km3 * K5 * K11 - K6 * K9 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K4 * Km3 - 2 * K6 * K9 * Km9 * K12 * K13 ^ 2 * K1 * K8 * K2 * K7 * K5 * K11 - ...
123  K6 * K9 * Km9 * K11 ^ 2 * K13 ^ 2 * K1 * K8 * K2 * Km3 * Km12 - K6 * K9 * Km9 * K11 ^ 2 * K13 ^ 2 * K1 * K8 * K2 * K7 * Km12 + 2 * K6 * K9 * K1 * K11 * K13 * Km12 * K8 * K2 * Km3 * K5 * K12 * Km11 - ...
124  K6 * K9 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K4 * K7 - 2 * K6 * K9 ^ 2 * K1 * K11 * K13 * Km12 * K4 * K7 * K5 * K12 * Km11 + 2 * K6 * K9 * K1 * K11 * K13 ^ 2 * Km12 * K8 * K2 * Km3 * K5 * K12 + ...
125  2 * K6 * K9 * K1 * K11 * K13 * Km12 * K8 * K2 * K7 * K5 * K12 * Km11 + 2 * K6 * K9 * K1 * K11 * K13 ^ 2 * Km12 * K8 * K2 * K7 * K5 * K12 - 2 * K6 * K9 ^ 2 * K1 * K11 * K13 * Km12 * K4 * Km3 * K5 * K12 * Km11 - ...
126  2 * K6 * K9 ^ 2 * K1 * K11 * K13 ^ 2 * Km12 * K4 * Km3 * K5 * K12 - K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K4 * K7 - 2 * K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K4 * K7 * K13 - ...
127  K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K3 * K7 - 2 * K6 * K9 ^ 2 * K1 * K11 * K13 ^ 2 * Km12 * K4 * K7 * K5 * K12 - K6 * K9 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K3 * K7 - ...
128  2 * K6 * K9 ^ 2 * K1 * K11 * K13 * Km12 * K3 * K7 * K5 * K12 * Km11 - 2 * K6 * K9 ^ 2 * K1 * K11 * K13 ^ 2 * Km12 * K3 * K7 * K5 * K12 + 2 * K6 * K9 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K8 * K2 * Km3 * K13 + ...
129  2 * K6 * K9 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K8 * K2 * K7 * K13 - K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K4 * Km3 - 2 * K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K4 * Km3 * K13 + ...
130  2 * Km10 * K2 * K1 * Km9 * K12 * K13 ^ 2 * K9 * K4 * Km3 * K5 * K11 + 2 * Km10 * K2 * K1 * Km9 * K12 * K13 ^ 2 * K9 * K4 * K7 * K5 * K11 + 2 * Km10 * K2 * K1 * Km9 * K12 * K13 ^ 2 * K9 * K3 * K7 * K5 * K11 - ...
131  2 * Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K8 * Km3 * Km12 - 2 * K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K3 * K7 * K13 - K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K4 * Km3 - ...
132  K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K4 * K7 - K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K3 * K7 - 4 * Km10 * K2 ^ 2 * K1 * Km9 * K12 * Km11 * K8 * Km3 * K5 * K11 * K13 - ...
133  4 * Km10 * K2 ^ 2 * K1 * Km9 * K12 * Km11 * K8 * K7 * K5 * K11 * K13 + 2 * Km10 * K2 * K1 * Km9 * K12 * Km11 * K9 * K4 * Km3 * K5 * K11 * K13 + 2 * Km10 * K2 * K1 * Km9 * K12 * Km11 * K9 * K4 * K7 * K5 * K11 * K13 + ...
134  2 * Km10 * K2 * K1 * Km9 * K12 * Km11 * K9 * K3 * K7 * K5 * K11 * K13 - 4 * Km10 * K2 ^ 2 * K1 * Km9 * K12 * K13 ^ 2 * K8 * Km3 * K5 * K11 - 4 * Km10 * K2 ^ 2 * K1 * Km9 * K12 * K13 ^ 2 * K8 * K7 * K5 * K11 - ...
135  Km10 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K9 * K4 * Km3 - 2 * Km10 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K9 * K4 * Km3 * K13 - Km10 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K9 * K4 * K7 - ...
136  2 * Km10 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K9 * K4 * K7 * K13 - Km10 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K9 * K3 * K7 - 2 * Km10 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K9 * K3 * K7 * K13 - ...
137  2 * Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K8 * K7 * Km12 + 2 * Km10 * K2 ^ 2 * K1 * K11 * K13 * Km12 * K8 * Km3 * K5 * K12 * Km11 + 2 * Km10 * K2 ^ 2 * K1 * K11 * K13 ^ 2 * Km12 * K8 * Km3 * K5 * K12 + ...
138  2 * Km10 * K2 ^ 2 * K1 * K11 * K13 * Km12 * K8 * K7 * K5 * K12 * Km11 + 2 * Km10 * K2 ^ 2 * K1 * K11 * K13 ^ 2 * Km12 * K8 * K7 * K5 * K12 - Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K9 * K4 * Km3 - ...
139  2 * Km10 * K2 * K1 * K11 * K13 * Km12 * K9 * K4 * Km3 * K5 * K12 * Km11 - 2 * Km10 * K2 * K1 * K11 * K13 ^ 2 * Km12 * K9 * K4 * Km3 * K5 * K12 - Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K9 * K4 * K7 - ...
140  2 * Km10 * K2 * K1 * K11 * K13 * Km12 * K9 * K4 * K7 * K5 * K12 * Km11 - 2 * Km10 * K2 * K1 * K11 * K13 ^ 2 * Km12 * K9 * K4 * K7 * K5 * K12 - Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K9 * K3 * K7 - ...
141  2 * Km10 * K2 * K1 * K11 * K13 * Km12 * K9 * K3 * K7 * K5 * K12 * Km11 - 2 * Km10 * K2 * K1 * K11 * K13 ^ 2 * Km12 * K9 * K3 * K7 * K5 * K12 + 2 * Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K8 * Km3 * K13 + ...
142  2 * Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 * K8 * K7 * K13 + K6 * K9 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K8 * K2 * Km3 + K6 * K9 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K8 * K2 * K7 + ...
143  K6 * K9 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K8 * K2 * Km3 + K6 * K9 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K8 * K2 * K7 + K6 * K9 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K8 * K2 * Km3 + ...
144  K6 * K9 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K8 * K2 * K7 - Km10 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K9 * K4 * Km3 - Km10 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K9 * K4 * K7 - ...
145  Km10 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K9 * K3 * K7 - 2 * Km8 * K2 * K1 * Km9 * K12 * Km11 * K9 * K3 * K7 * K5 * K11 * K13 + Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 ^ 2 * K8 * Km3 + ...
146  Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 ^ 2 * K8 * K7 + Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K4 * Km3 * Km12 + Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K4 * K7 * Km12 + ...
147  Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K3 * K7 * Km12 + Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K8 * Km3 + Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K8 * K7 + ...
148  Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K8 * Km3 + Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K8 * K7 + Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K8 * Km3 + ...
149  Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K8 * K7 + Km8 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 ^ 2 * K9 * K3 * K7 + Km8 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * Km11 ^ 2 * K9 * K3 * K7 + ...
150  Km8 * K2 * K1 * K5 ^ 2 * K12 ^ 2 * K13 ^ 2 * K9 * K3 * K7);
151 /* Koeffizient vor x^(n+3) */
152 anp3 = (-2 * Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K9 * K4 * K7 * K5 - 2 * Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K9 * K3 * K7 * K5 + 2 * Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 * Km11 * K8 * Km3 * K11 * K13 + ...
153  2 * Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 * Km11 * K8 * K7 * K11 * K13 - 2 * Km10 * K2 * K1 * K5 ^ 2 * K12 * Km11 * K9 * K4 * Km3 * K11 * K13 - 2 * Km10 * K2 * K1 * K5 ^ 2 * K12 * Km11 * K9 * K4 * K7 * K11 * K13 - ...
154  2 * Km10 * K2 * K1 * K5 ^ 2 * K12 * Km11 * K9 * K3 * K7 * K11 * K13 + 2 * Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K8 * Km3 * K11 - Km8 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K3 * K7 * K5 + ...
155  2 * Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K8 * K7 * K11 - 2 * Km10 * K2 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K9 * K4 * Km3 * K11 - 2 * Km10 * K2 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K9 * K4 * K7 * K11 - ...
156  2 * Km10 * K2 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K9 * K3 * K7 * K11 - K6 * K9 * Km9 * K11 ^ 2 * K13 ^ 2 * K1 * K8 * K2 * K7 * K5 + 2 * Km8 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K9 * K3 * K7 * K5 + ...
157  2 * Km8 * K2 * K1 * K5 ^ 2 * K12 * Km11 * K9 * K3 * K7 * K11 * K13 + 2 * Km8 * K2 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K9 * K3 * K7 * K11 - K6 * K9 * Km9 * K11 ^ 2 * K13 ^ 2 * K1 * K8 * K2 * Km3 * K5 + ...
158  2 * K6 * K9 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K8 * K2 * Km3 * K5 + 2 * K6 * K9 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K8 * K2 * K7 * K5 - 2 * K6 * K9 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K4 * Km3 * K5 - ...
159  2 * K6 * K9 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K4 * K7 * K5 - 2 * K6 * K9 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K3 * K7 * K5 + 2 * K6 * K9 * K1 * K5 ^ 2 * K12 * Km11 * K8 * K2 * Km3 * K11 * K13 + ...
160  2 * K6 * K9 * K1 * K5 ^ 2 * K12 * Km11 * K8 * K2 * K7 * K11 * K13 - 2 * K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 * Km11 * K4 * Km3 * K11 * K13 - 2 * K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 * Km11 * K4 * K7 * K11 * K13 - ...
161  2 * K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 * Km11 * K3 * K7 * K11 * K13 + 2 * K6 * K9 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K8 * K2 * Km3 * K11 + 2 * K6 * K9 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K8 * K2 * K7 * K11 - ...
162  2 * K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K4 * Km3 * K11 - 2 * K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K4 * K7 * K11 - 2 * K6 * K9 ^ 2 * K1 * K5 ^ 2 * K12 * K13 ^ 2 * K3 * K7 * K11 - ...
163  2 * Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K8 * Km3 * K5 - 2 * Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K8 * K7 * K5 + 2 * Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K8 * Km3 * K5 + ...
164  2 * Km10 * K2 ^ 2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K8 * K7 * K5 - 2 * Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km12 * K9 * K4 * Km3 * K5 + Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K4 * Km3 * K5 + ...
165  Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K4 * K7 * K5 + Km10 * K2 * K1 * K11 ^ 2 * K13 ^ 2 * Km9 * K9 * K3 * K7 * K5);
166 /* Koeffizient vor x^(n+4) */
167 anp4 = (-Km10 * K2 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K9 * K3 * K7 - K6 * K9 ^ 2 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K3 * K7 - Km10 * K2 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K9 * K4 * K7 + ...
168  Km8 * K2 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K9 * K3 * K7 + K6 * K9 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K8 * K2 * K7 + Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K8 * Km3 + ...
169  Km10 * K2 ^ 2 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K8 * K7 - K6 * K9 ^ 2 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K4 * Km3 - K6 * K9 ^ 2 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K4 * K7 + ...
170  K6 * K9 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K8 * K2 * Km3 - Km10 * K2 * K1 * K5 ^ 2 * K11 ^ 2 * K13 ^ 2 * K9 * K4 * Km3);
171 /* Koeffizinten in der Gr��enordnung von 1e-21
172  * Multiplikation der Funktionswerte mit Zehnerpotenzen */
173 while (max([anp4 anp3 anp2 anp1 an a1 a2 a3 a4]) < 1.0)
174  a1 = 10*a1;
175  a2 = 10*a2;
176  a3 = 10*a3;
177  a4 = 10*a4;
178  an = 10*an;
179  anp1 = 10*anp1;
180  anp2 = 10*anp2;
181  anp3 = 10*anp3;
182  anp4 = 10*anp4;
183 end
184 
185 /* x^1 ausgeklammert */
186 polynom = @(x) anp4*x.^(n+3) + anp3*x.^(n+2) + anp2*x.^(n+1) + anp1*x.^(n) + an*x.^(n-1) + ...
187  a1 + a2*x + a3*x.^2 + a4*x.^3;
188 
189 
190 /* Bestimme Nullstelle des Polynoms -> Konzentration von x_a */
191 options = optimoptions(" fsolve "," TolFun ",1e-15," Display "," None ");
192 xa = fsolve(polynom,0.2,options);
193 
194 /* Plotten des Polynoms -> Visualisierung der Lage der Nullstellen */
195 if doplot
196  x = linspace(0,xa+1000*eps,10000);
197  plot(x,polynom(x)," b ")
198 end
199 /* Fuer n = 3.818 fallen death state und transition state ann�hernd zusammen
200  * und polynom beruehrt die x-Achse
201  * Fuer kleiner werdende n wandert der transition state Richtung life state */
202 
203 /* Konzentration von y_a im Death State */
204 ya = K9*Km9/K2*(K12 + K11*K13/(Km11+K13)*xa)/(Km9*K12+xa*((Km9-Km12)*K11*K13/(Km11+K13)-K5*K12)-K5*K11*K13/(Km11+K13)*xa^2)-K9/K2;
205 /* Konzentration von x_i im Death State */
206 xi = Km9/(K2*ya+K9);
207 /* Konzentration von y_i im Death State */
208 yi = Km10/(K1*xa^n+K10);
209 /* Konzentration von iap im Death State */
210 iap = Km8/(K8+ya*(K4+K3*K7/(Km3+K7)));
211 /* Konzentration von bar im Death State */
212 bar = Km12/(K12+(K11*K13)/(Km11+K13)*xa);
213 /* Konzentration von y_a~iap im Death State */
214 yb = K3*ya*iap/(Km3+K7);
215 /* Konzentration von x_a~bar im Death State */
216 xb = K11*xa*bar/(Km11+K13);
217 
218 ss(:,1) = [xa;ya;xi;yi;iap;bar;yb;xb];
219 ss(:,2) = [0;0;Km9/K9;Km10/K10;Km8/K8;Km12/K12;0;0];
220 
221 /* Probe -> Einsetzen in Reaktions-System */
222 chk = [K2*xi*ya - K5*xa - K11*xa*bar + Km11*xb; ...
223 K1*yi*xa^n - K6*ya - K3*ya*iap + Km3*yb; ...
224 -K2*xi*ya - K9*xi + Km9; ...
225 -K1*yi*xa^n - K10*yi + Km10; ...
226 -K3*ya*iap - K8*iap + Km8 - K4*ya*iap + Km3*yb; ...
227 -K11*xa*bar + Km11*xb - K12*bar + Km12; ...
228 K3*ya*iap - Km3*yb - K7*yb; ...
229 K11*xa*bar - Km11*xb - K13 *xb];
230 if any(abs(chk) > 200*eps)
231  warning(" Attention! One or more roots for system steady states not zero in machine precision: %g ",max(abs(chk)));
232 end
233 }
234 
235 };
236 };
models.pcdi.PCDIModel.getSteadyStates
function ss = getSteadyStates(n)
Definition: getSteadyStates.m:20
PCDIModel.m